Geodesic
On a complete orthonormal system
Sbornik. Mathematics, Tome 28 (1976) no. 3, pp. 315-324 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we construct in $L_2(0,1)$ a complete orthonormal system $\{\psi_n(x)\}_{n=1}^\infty$ for which every series $\sum_{n=1}^\infty c_n\psi_n(x)$ whose coefficients satisfy the condition $\sum_{n=1}^\infty c_n^2=\infty$ diverges on a set of positive measure. Bibliography: 6 titles. 
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     author = {B. S. Kashin},
     title = {On a~complete orthonormal system},
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     pages = {315--324},
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     volume = {28},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_28_3_a3/}
}
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B. S. Kashin. On a complete orthonormal system. Sbornik. Mathematics, Tome 28 (1976) no. 3, pp. 315-324. http://geodesic.mathdoc.fr/item/SM_1976_28_3_a3/

[1] A. A. Talalyan, “Predstavlenie izmerimykh funktsii ryadami”, Uspekhi matem. nauk, XV:5 (100) (1960), 77–141 | MR | Zbl

[2] P. L. Ulyanov, “Predstavlenie funktsii ryadami i klassy $\varphi(L)$”, Uspekhi matem. nauk, XXVII:2 (164) (1972), 3–52 | MR | Zbl

[3] A. Zigmund, Trigonometricheskie ryady, t. 1, Mir, Moskva, 1965 | MR | Zbl

[4] S. Kachmazh, G. Shteingauz, Teoriya ortogonalnykh ryadov, Fizmatgiz, Moskva, 1958 | MR

[5] G. Khardi, D. Littlvud, G. Polia, Neravenstva, IL, Moskva, 1948 | MR

[6] P. L. Ulyanov, “Reshennye i nereshennye problemy teorii trigonometricheskikh i ortogonalnykh ryadov”, Uspekhi matem. nauk, XIX:1 (115) (1964), 3–69 | MR | Zbl